Question

What would be the length of diagonal of a square plot whose area is equal to the area of rectangular plot of 50 m length and 40.5 m?

Answer 1

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Answer 2

Answer: The length of the diagonal is 63.64 metres.

Step-by-step explanation: As shown in the attached figure, square ABCD has area equal to the area of rectangle EFGH with length 50 m and breadth 40.5 m. We need to find the length of diagonal AC of square ABCD.

Now, area of rectangle ABCD= length × breadth

                                                 = 50 m × 40.5 m

                                                 = 2025 m².

Let the length of a side of square ABCD be 'h' m. Since the square and rectangle have equal areas, so

h × h = 2025 m²

i.e., h² = 2025 m².

Since every angle of a square is a right angle, so Δ ABC will be a right angled triangle, and hence, applying Pythagoras theorem we can write

AC² = AB² + BC² = h² + h² = 2025+2025= 4050 m²,

which gives

AC= 63.64 m.

Thus, the length of diagonal of the square is 63.64 metres.